The 6ft 4in no 8, who hails from Oban, worked his way through the age grades for Glasgow, then Edinburgh and Scotland and is in the Scotland under-20 squad for this year's 6 Nations.
Bradbury made his full pro team debut for the club, in the starting XV, in October's Guinness PRO12 fixture at the RDS against Leinster.
He said: "It was a great experience and really opened my eyes to the intensity of the pro game. Training with the guys is one thing but that game was a snapshot of what a step up it is.
"This is something I've been working towards for years and I just want to keep on pushing, training to the best of my ability and to keep on raising my game."
Like all the Academy players, Bradbury has benefited from being mentored by a senior player in his position, in his case captain Mike Coman.
He said: "Mike has definitely helped me - we discuss my game, how it's going and where I can improve.
"Next season I really want to work hard to establish myself as a player and get as much game time as I can."
Joining the club at the start of next season, also on a two-year contract, from London Wasps will be winger Will Helu.
The 19-times capped Tongan international - part of the squad that beat France in Rugby World Cup 2011 - scored seven tries in Wasp's run to the semi-finals of the Challenge Cup last season.
Helu said: "I jumped at the chance to move to Edinburgh, after meeting Alan and hearing him speak about the potential of the club - and obviously you guys are doing well, especially winning the 1872 Cup last weekend.
"I think I've a lot to give on the field - a lot of ball in hand, running rugby."
Though his experience of playing in Scotland is limited to an outing in Aberdeen, when Tonga beat the national side at Pittodrie, he is looking forward to renewing his acquaintance with a former team mate on arrival at BT Murrayfield.
He said: "I played with Neil Cochrane at Wasps last season and it'll be good to link up with a familiar face."
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland